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Question

The foot of the perpendicular on the line 3 x plus y equals lambda drown from the origin is C if the line cuts the x-axis and y-axis at A and B respectively then BC : CA is

  1. 1:3    
  2. 3:1    
  3. 1:9    
  4. 9:1    

The correct answer is: 9:1


    Let direction ratios of the required line be <a, b, c>
    Therefore a - 2 b - 2 c = 0
    And 2 b + c = 0
    Þ c = - 2 b
    a - 2 b + 4b = 0 Þ a = - 2 b
    Therefore direction ratios of the required line are <- 2b, b, - 2b> = <2, - 1, 2>
    direction cosines of the required line
    open parentheses fraction numerator 2 over denominator square root of 2 to the power of 2 end exponent plus 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end root end fraction comma fraction numerator negative 1 over denominator square root of 2 to the power of 2 end exponent plus 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end root end fraction comma fraction numerator 2 over denominator square root of 2 to the power of 2 end exponent plus 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end root end fraction close parentheses = open parentheses fraction numerator 2 over denominator 3 end fraction comma fraction numerator negative 1 over denominator 3 end fraction comma fraction numerator 2 over denominator 3 end fraction close parentheses

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